I don’t think the execution will take place. I will be very surprised if this killer does not have a fleet of lawyers petitioning for his delay.
There is a limit to the number of appeals you can file. Matters of fact cannot be appealed after the trial and sooner or later all matters of law are exhausted. A lawyer would have to make a non trivial representation that some or another legal irregularity occurred that prevents his execution. All such appeals should already have been filed. Sometimes lawyers invent novel points of law, but at best those can only buy him a day or so.